Positioning devices serve for the most varied positioning tasks, in which probes, sensors, grippers, tools, and the like must be introduced at a specific place determined in advance and in a defined position. In flow measurement segments, for example, the most varied flow measurement probes, such as pressure, temperature, anemometer, directional and special measurement probes must be positioned at measurement sites precisely indicated in advance. The positioning, which must be conducted very exactly depending on the measurement task, is frequently made difficult by special environmental conditions, such as, for example, high temperatures. In the case of probes with probe heads turned away from the probe axis, a movement along the probe axis and rotationally around the probe axis is at least necessary, in order to align the probe head as desired on the object to be measured. Thus, frequently, displacement paths of several dozen cm and rotations of +/-180 angular degrees are necessary. Such positioning devices are controlled for the most part with the help of a computer programmed according to the positioning task. In order to be able to conduct measurements or positionings in spatially limited installation conditions, devices with compact dimensions are desired.